| 1 | Suppression of explosion by polynomial noise for nonlinear differential systems显示文摘In this paper, we study the problem of the suppression of explosion by noise for nonlinear non-autonomous differential systems. For a deterministic non-autonomous differential system dx(t) =f(x(t), t)dt, which can explode at a finite time, we introduce polynomial noise and study the perturbed system dx(t) = f(x(t), t)dt + h(t)^(1/2)|x(t)|βAx(t)d B(t). We demonstrate that the polynomial noise can not only guarantee the existence and uniqueness of the global solution for the perturbed system, but can also make almost every path of the global solution grow at most with a certain general rate and even decay with a certain general rate(including super-exponential, exponential, and polynomial rates) under specific weak conditions. | Lichao FENG Shoumei LI Renming SONG Yemo LI | 2018 | Science China(Information Sciences)2018，61，7： | 1 |
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